Open Access

# Strong base for fuzzy topology

### Abstract

It is known that a base for a traditional topology, or for a $L$-topology, $\tau$, is a subset ${\mathcal B}$ of $\tau$ with the property that every element $G\in \tau$ can be written as a union of elements of ${\mathcal B}$. In the classical case it is equivalent to say that $G\in \tau$ if and only if for any $x\in G$ we have $B\in {\mathcal B}$ satisfying $x\in B \subseteq G$. This latter property is taken as the foundation for a notion of strong base for a $L$-topology. Characteristic properties of a strong base are given and among other results it is shown that a strong base is a base, but not conversely.

### Article Information

 Title Strong base for fuzzy topology Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 4, 350-355 MathSciNet MR2907363 Copyright The Author(s) 2011 (CC BY-SA)

### Authors Information

A. A. Rakhimov
Tashkent Institute of Railways and Engineering, Tashkent, Uzbekistan; Karadeniz Technical University, Turkey

F. M. Zakirov

### Citation Example

A. A. Rakhimov and F. M. Zakirov, Strong base for fuzzy topology, Methods Funct. Anal. Topology 17 (2011), no. 4, 350-355.

### BibTex

@article {MFAT582,
AUTHOR = {Rakhimov, A. A. and Zakirov, F. M.},
TITLE = {Strong base for fuzzy topology},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {4},
PAGES = {350-355},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=582},
}